KDTree should support Haversine Metric

Related to #12552

Using the Haversine metric with the KDTree produces an error

haversineMetric = DistanceMetric.get_metric('haversine')
coordsKdTree = KDTree(coords, leaf_size =1e3, metric = haversineMetric)

ValueError                                Traceback (most recent call last)
<ipython-input-15-fa4421f977f6> in <module>
     10 #Create KD tree with haversine metric
     11 haversineMetric = DistanceMetric.get_metric('haversine')
---> 12 coordsKdTree = KDTree(coords, leaf_size =1e3, metric = haversineMetric)

sklearn/neighbors/_binary_tree.pxi in sklearn.neighbors._kd_tree.BinaryTree.__init__()

ValueError: metric HaversineDistance is not valid for KDTree

[rth]

Though it was added to Ball Tree by Jake at the time of the original implementation (https://github.com/scikit-learn/scikit-learn/commit/01fce7661632c7898feaf9a2e1dc3ce97a91473d, https://github.com/scikit-learn/scikit-learn/pull/1732) and none of the reviewers disagreed. So maybe we are missing something. I guess we could always try to find an counter-example to the triangle inequality with Haversine distance to be sure 😃

[rth]

My math on the sphere is pretty bad, and it sounds like you are right 😃

there are other reasons, why the haversine metric should be used with caution with KD-Trees:

The k-d-tree can (to the best of my knowledge)

Thanks for investigating! Probably safter to keep this closed then (though the latter part needs better citations ^^)?